Abstract

A subset R ⊆ S 3 will be called (associatively) admissible if there exists a binary operation * defined on S such that x * ( y * z ) = ( x * y ) * z iff ( x, y, z ) ∈ R . If S is finite, card( S ) = n , R ⊆ S 3 , card( R ) = r and r ⩽ n /4−3/4 or n 3 − n /4 + 1/2 ⩽ r, then R is admissible. There exists an admissible subset for any 0 ⩽ r ⩽ n 3 and a non-admissible subset for any 3 n ≤ r ⩽ n 3 − n +2.

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